Scaling, Multiscaling, and Nontrivial Exponents in Inelastic Collision Processes

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dc.creatorBen-Naim, E.
dc.creatorKrapivsky, P. L.
dc.date2002-02-20
dc.date.accessioned2026-07-07T02:44:28Z
dc.date.available2026-07-07T02:44:28Z
dc.descriptionWe investigate velocity statistics of homogeneous inelastic gases using the Boltzmann equation. Employing an approximate uniform collision rate, we obtain analytic results valid in arbitrary dimension. In the freely evolving case, the velocity distribution is characterized by an algebraic large velocity tail, P(v,t) ~ v^{-sigma}. The exponent sigma(d,epsilon), a nontrivial root of an integral equation, varies continuously with the spatial dimension, d, and the dissipation coefficient, epsilon. Although the velocity distribution follows a scaling form, its moments exhibit multiscaling asymptotic behavior. Furthermore, the velocity autocorrelation function decays algebraically with time, A(t)=<v(0)v(t)> ~ t^{-alpha}, with a non-universal dissipation-dependent exponent alpha=1/epsilon. In the forced case, the steady state Fourier transform is obtained via a cumulant expansion. Even in this case, velocity correlations develop and the velocity distribution is non-Maxwellian.
dc.description10 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0202332
dc.identifierhttp://arxiv.org/abs/cond-mat/0202332
dc.identifierPhys. Rev. E 66, 011309 (2002)
dc.identifierdoi:10.1103/PhysRevE.66.011309
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/18936
dc.subjectStatistical Mechanics
dc.subjectSoft Condensed Matter
dc.subjectCellular Automata and Lattice Gases
dc.titleScaling, Multiscaling, and Nontrivial Exponents in Inelastic Collision Processes
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